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References

Published online by Cambridge University Press:  05 December 2015

François G. Schmitt
Affiliation:
Centre National de la Recherche Scientifique (CNRS), Paris
Yongxiang Huang
Affiliation:
Xiamen University
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Stochastic Analysis of Scaling Time Series
From Turbulence Theory to Applications
, pp. 185 - 201
Publisher: Cambridge University Press
Print publication year: 2016

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References

Abry, P., Chainais, P., Coutin, L., and Pipiras, V. 2009. Multifractal random walks as fractional Wiener integrals. IEEE Trans. Inform. Theory, 55(8), 3825–3846.CrossRefGoogle Scholar
Ahlers, G., Grossmann, S., and Lohse, D. 2009. Heat transfer and large scale dynamics in turbulent Rayleigh-Bénard convection. Rev. Mod. Phys., 81(2), 503–537.CrossRefGoogle Scholar
Alexakis, A., and Doering, C. R. 2006. Energy and e nstrophy dissipation in steady state 2D turbulence. Phys. Lett. A, 359(6), 652–657.CrossRefGoogle Scholar
Anh, Vo V., Leonenko, Nikolai N., and Shieh, Narn-Rueih. 2008. Multifractality of products of geometric Ornstein-Uhlenbeck-type processes. Adv. Appl. Prob., 40, 1129–1156.CrossRefGoogle Scholar
Anselmet, F., Gagne, Y., Hopfinger, E. J., and Antonia, R. A. 1984. High-order velocity structure functions in turbulent shear flows. J. Fluid Mech., 140, 63–89.CrossRefGoogle Scholar
Applebaum, D. 2004. Lévy processes and stochastic calculus. Cambridge University Press.CrossRefGoogle Scholar
Apt, J. 2007. The spectrum of power from wind turbines. J. Power Sources, 169(2), 369–374.CrossRefGoogle Scholar
Arnéodo, A., Baudet, C., Belin, F., Benzi, R., Castaing, B., Chabaud, B., Chavarria, R., Ciliberto, S., Camussi, R., and Chilla, F. 1996. Structure functions in turbulence, in various flow configurations, at Reynolds number between 30 and 5000, using extended self-similarity. Europhys. Lett., 34(6), 411–416.CrossRefGoogle Scholar
Arnéodo, A., Benzi, R., Berg, J., Biferale, L., Bodenschatz, E., Busse, A., Calzavarini, E., Castaing, B., Cencini, M., Chevillard, L., Fisher, R. T., Grauer, R., Homann, H., Lamb, D., Lanotte, A. S., Lévêque, E., Luthi, B., Mann, J., Mordant, N., Muller, W.-C., Ott, S., Ouellette, N. T., Pinton, J.-F., Pope, S. B., Roux, S. G., Toschi, F., Xu, H., and Yeung, P. K. 2008. Universal intermittent properties of particle trajectories in highly turbulent flows. Phys. Rev. Lett., 100(25), 254504.CrossRefGoogle ScholarPubMed
Arrault, J., Arnéodo, A., Davis, A., and Marshak, A. 1997. Wavelet based multifractal analysis of rough surfaces: application to cloud models and satellite data. Phys. Rev. Lett., 79(1), 75–78.CrossRefGoogle Scholar
Ashkenazi, S., and Steinberg, V. 1999. Spectra and statistics of velocity and temperature fluctuations in turbulent convection. Phys. Rev. Lett., 83(23), 4760–4763.CrossRefGoogle Scholar
Bacry, E., and Muzy, J.-F. 2003. Log-infinitely divisible multifractal processes. Commun. Math. Phys., 236(3), 449–475.CrossRefGoogle Scholar
Bacry, E., Delour, J., and Muzy, J. F. 2001. A multifractal random walk. Phys. Rev. E, 64(2), 026103.CrossRefGoogle ScholarPubMed
Balocchi, R., Menicucci, D., Santarcangelo, E., Sebastiani, L., Gemignani, A., Ghelarducci, B., and Varanini, M. 2004. Deriving the respiratory sinus arrhythmia from the heartbeat time series using empirical mode decomposition. Chaos Soliton Fract., 20(1), 171–177.CrossRefGoogle Scholar
Barabási, A.-L., Szépfalusy, P., and Vicsek, T. 1991. Multifractal spectra of multi-affine functions. Physica A, 178(1), 17–28.CrossRefGoogle Scholar
Bardet, J. M., and Kammoun, I. 2008. Asymptotic properties of the detrended fluctuation analysis of long-range-dependent processes. IEEE Trans. Inform. Theory, 54(5), 2041–2052.CrossRefGoogle Scholar
Barral, J., and Mandelbrot, B. B. 2002. Multifractal products of cylindrical pulses. Probab. Theory Related Fields, 124(3), 409–430.CrossRefGoogle Scholar
Bashan, A., Bartsch, R., Kantelhardt, J.W., and Havlin, S. 2008. Comparison of detrending methods for fluctuation analysis. Physica A, 387(21), 5080–5090.CrossRefGoogle Scholar
Batchelor, G. K. 1953. The theory of homogeneous turbulence. Cambridge University Press.Google Scholar
Batchelor, G. K., and Townsend, A. A. 1949. The nature of turbulent motion at large wavenumbers. Proc. R. Soc. A, 199(1057), 238–255.CrossRefGoogle Scholar
Battjes, J. A. 1988. Surf zone dynamics. Annu. Rev. Fluid Mech., 20(1), 257–291.CrossRefGoogle Scholar
Bec, J., Biferale, L., Cencini, M., Lanotte, A. S., and Toschi, F. 2006. Effects of vortex filaments on the velocity of tracers and heavy particles in turbulence. Phys. Fluids, 18, 081702.CrossRefGoogle Scholar
Bec, J., Homann, H., and Krstulovic, G. 2014. Clustering, fronts, and heat transfer in turbulent suspensions of heavy particles. Phys. Rev. Lett., 112, 234503.CrossRefGoogle ScholarPubMed
Beck, C. 2007. Statistics of three-dimensional Lagrangian turbulence. Phys. Rev. Lett., 98(6), 064502.CrossRefGoogle ScholarPubMed
Benzi, R., Paladin, G., Vulpiani, A., and Parisi, G. 1984. On the multifractal nature of fully developed turbulence and chaotic systems. J. Phys. A, 17, 3521–3531.CrossRefGoogle Scholar
Benzi, R., Ciliberto, S., Tripiccione, R., Baudet, C., Massaioli, F., and Succi, S. 1993a. Extended self-similarity in turbulent flows. Phys. Rev. E, 48(1), 29–32.CrossRefGoogle ScholarPubMed
Benzi, R., Biferale, L., Crisanti, A., Paladin, G., Vergassola, M., and Vulpiani, A. 1993b. A random process for the construction of multiaffine fields. Physica D, 65(4), 352–358.CrossRefGoogle Scholar
Benzi, R., Ciliberto, S., Baudet, C., and Chavarria, G. R. 1995. On the scaling of threedimensional homogeneous and isotropic turbulence. Physica D, 80(4), 385–398.CrossRefGoogle Scholar
Benzi, R., Biferale, L., Calzavarini, E., Lohse, D., and Toschi, F. 2009. Velocity-gradient statistics along particle trajectories in turbulent flows: the refined similarity hypothesis in the Lagrangian frame. Phys. Rev. E, 80(6), 066318.CrossRefGoogle ScholarPubMed
Beran, J. 1994. Statistics for long-memory processes. CRC Press.Google Scholar
Berg, J., Ott, S., Mann, J., and Lüthi, B. 2009. Experimental investigation of Lagrangian structure functions in turbulence. Phys. Rev. E, 80(2), 026316.CrossRefGoogle ScholarPubMed
Bernard, D. 2000. Influence of friction on the direct cascade of the 2d forced turbulence. Europhys. Lett., 50, 333–339.CrossRefGoogle Scholar
Bernard, P. S., and Wallace, J. M. 2002. Turbulent flow: analysis, measurement, and prediction. John Wiley & Sons.Google Scholar
Biagini, F., Hu, Y., Oksendal, B., and Zhang, T. 2008. Stochastic calculus for fractional Brownian motion and applications. Springer Verlag.CrossRefGoogle Scholar
Biferale, L., Boffetta, G., Celani, A., Crisanti, A., and Vulpiani, A. 1998. Mimicking a turbulent signal: sequential multiaffine processes. Phys. Rev. E, 57, R6261–R6264.CrossRefGoogle Scholar
Biferale, L., Cencini, M., Lanotte, A. S., and Vergni, D. 2003. Inverse velocity statistics in two-dimensional turbulence. Phys. Fluids, 15(4), 1012–1020.CrossRefGoogle Scholar
Biferale, L., Boffetta, G., Celani, A., Devenish, B. J., Lanotte, A., and Toschi, F. 2004. Multifractal statistics of Lagrangian velocity and acceleration in turbulence. Phys. Rev. Lett., 93(6), 064502.CrossRefGoogle ScholarPubMed
Blain, S., Guillou, J., Treguer, P., Woerther, P., Delauney, L., Follenfant, E., Gontier, O., Hamon, M., Leilde, B., Masson, A., Tartub, C., and Vuillemin, R. 2004. High frequency monitoring of the coastal environment using the marel buoy. J. Environ. Monit., 6, 569–575.CrossRefGoogle ScholarPubMed
Boffetta, G. 2007. Energy and enstrophy fluxes in the double cascade of two-dimensional turbulence. J. Fluid Mech., 589, 253–260.CrossRefGoogle Scholar
Boffetta, G., and Ecke, R. E. 2012. Two-Dimensional Turbulence. Annu. Rev. Fluid Mech., 44, 427–451.CrossRefGoogle Scholar
Boffetta, G., and Musacchio, S. 2010. Evidence for the double cascade scenario in twodimensional turbulence. Phys. Rev. E, 82(1), 016307.CrossRefGoogle Scholar
Boffetta, G., Celani, A., Musacchio, S., and Vergassola, M. 2002. Intermittency in twodimensional Ekman-Navier-Stokes turbulence. Phys. Rev. E, 66(2), 026304.CrossRefGoogle Scholar
Bolgiano, R. 1959. Turbulent spectra in a stably stratified atmosphere. J. Geophys. Res., 64, 2226–2229.CrossRefGoogle Scholar
Boettcher, F., Barth, S., and Peinke, J. 2007. Small and large scale fluctuations in atmospheric wind speeds. Stoch. Env. Res. Risk A., 21(3), 299–308.Google Scholar
Bouchet, F., and Venaille, A. 2012. Statistical mechanics of two-dimensional and geophysical flows. Phys. Rep., 515, 227–295.CrossRefGoogle Scholar
Brown, E., and Ahlers, G. 2007. Large-scale circulation model for turbulent Rayleigh- Bénard convection. Phys. Rev. Lett., 98(Mar.), 134501.CrossRefGoogle ScholarPubMed
Brown, E., Nikolaenko, A., and Ahlers, G. 2005. Reorientation of the large-scale circulation in turbulent Rayleigh-Bénard convection. Phys. Rev. Lett., 95, 084503.CrossRefGoogle ScholarPubMed
Calif, R., and Schmitt, F. G. 2012. Modeling of atmospheric wind speed sequence using a lognormal continuous stochastic equation. J. Wind Eng. Ind. Aerodyn., 109, 1–8.CrossRefGoogle Scholar
Calif, R., and Schmitt, F. G. 2014. Multiscaling and joint multiscaling description of the atmospheric wind speed and the aggregate power output from a wind farm. Nonlinear Proc. Geoph., 21(2), 379–392.CrossRefGoogle Scholar
Calif, R., Schmitt, F. G., and Huang, Y. 2013. Multifractal description of wind power fluctuations using arbitrary order Hilbert spectral analysis. Physica A, 392, 4106–4120.CrossRefGoogle Scholar
Celani, A., Lanotte, A., Mazzino, A., and Vergassola, M. 2000. Universality and saturation of intermittency in passive scalar turbulence. Phys. Rev. Lett., 84, 2385–2388.CrossRefGoogle ScholarPubMed
Celani, A., Musacchio, S., and Vincenzi, D. 2010. Turbulence in more than two and less than three dimensions. Phys. Rev. Lett., 104(18), 184506.CrossRefGoogle ScholarPubMed
Chainais, P. 2006. Multidimensional infinitely divisible cascades. EPJ B, 51(2), 229–243.Google Scholar
Champagne, F. H. 1978. The fine-scale structure of the turbulent velocity field. J. Fluid Mech., 86(01), 67–108.CrossRefGoogle Scholar
Chang, G. C., and Dickey, T. D. 2001. Optical and physical variability on timescales from minutes to the seasonal cycle on the New England shelf: July 1996 to June 1997. J. Geophys. Res., 106, 9435–9453.CrossRefGoogle Scholar
Chavez, F. P., Pennington, J., Herlien, R., Jannasch, H., Thurmond, G., and Friederich, G. E. 1997. Moorings and drifters for real-time interdisciplinary oceanography. J. Atmos. Oceanic Technol., 14, 1199–1211.2.0.CO;2>CrossRefGoogle Scholar
Chen, J., Xu, Y. L., and Zhang, R. C. 2004. Modal parameter identification of Tsing Ma suspension bridge under Typhoon Victor: EMD-HT method. J. Wind Eng. Ind. Aerodyn., 92(10), 805–827.CrossRefGoogle Scholar
Chen, S. Y., and Cao, N. 1995. Inertial range scaling in turbulence. Phys. Rev. E, 52(6), 5757–5759.CrossRefGoogle ScholarPubMed
Chen, S. Y., Sreenivasan, K. R., Nelkin, M., and Cao, N. Z. 1997. Refined similarity hypothesis for transverse structure functions in fluid turbulence. Phys. Rev. Lett., 79(12), 2253–2256.CrossRefGoogle Scholar
Chen, S. Y., Ecke, R. E., Eyink, G. L., Wang, X., and Xiao, Z. 2003. Physical mechanism of the two-dimensional enstrophy cascade. Phys. Rev. Lett., 91(21), 214501.CrossRefGoogle ScholarPubMed
Chen, S. Y., Ecke, R. E., Eyink, G. L., Rivera, M., Wan, M., and Xiao, Z. 2006. Physical mechanism of the two-dimensional inverse energy cascade. Phys. Rev. Lett., 96(8), 84502.CrossRefGoogle ScholarPubMed
Chen, Z., Ivanov, P. Ch., Hu, K., and Stanley, H. E. 2002. Effect of nonstationarities on detrended fluctuation analysis. Phys. Rev. E, 65(4), 041107.CrossRefGoogle ScholarPubMed
Chevillard, L., and Meneveau, C. 2006. Lagrangian dynamics and statistical geometric structure of turbulence. Phys. Rev. Lett., 97(17), 174501.CrossRefGoogle ScholarPubMed
Chevillard, L., Roux, S. G., Lévêque, E., Mordant, N., Pinton, J.-F., and Arnéodo, A. 2003. Lagrangian velocity statistics in turbulent flows: Effects of dissipation. Phys. Rev. Lett., 91(21), 214502.CrossRefGoogle ScholarPubMed
Ching, E. S. C., Chui, K.-W., Shang, X. D., Qiu, X.-L., Tong, P., and Xia, K.-Q. 2004. Velocity and temperature cross-scaling in turbulent thermal convection. J. Turbul., 5, 027.CrossRefGoogle Scholar
Cioni, S., Ciliberto, S., and Sommeria, J. 1995. Temperature structure functions in turbulent convection at low Prandtl number. Europhys. Lett., 32, 413.CrossRefGoogle Scholar
Cohen, L. 1995. Time-frequency analysis. Englewood Cliffs, NJ: Prentice Hall PTR.Google Scholar
Collet, P., and Koukiou, F. 1992. Large deviations for multiplicative chaos. Commun. Math. Phys., 147(2), 329–342.CrossRefGoogle Scholar
Corrsin, S. 1951. On the spectrum of isotropic temperature fluctuations in an isotropic turbulence. J. Appl. Phys., 22, 469.CrossRefGoogle Scholar
Corrsin, S. 1975. Limitations of gradient transport models in random walks and in turbulence. Adv. Geophys., 18, 25–60.Google Scholar
Costa, A., Crespo, A., Navarro, J., Lizcano, G., Madsen, H., and Feitosa, E. 2008. A review on the young history of the wind power short-term prediction. Renew. Sust. Eenerg. Rev., 12(6), 1725–1744.Google Scholar
Coughlin, K. T., and Tung, K. K. 2004. 11-Year solar cycle in the stratosphere extracted by the empirical mode decomposition method. Adv. Space Res., 34(2), 323–329.CrossRefGoogle Scholar
Dahlstedt, K., and Jensen, H. J. 2005. Fluctuation spectrum and size scaling of river flow and level. Physica A, 348, 596–610.CrossRefGoogle Scholar
Daubechies, I. 1992. Ten lectures on wavelets. Philadelphia: SIAM.CrossRefGoogle Scholar
Davidson, P. A., and Pearson, B. R. 2005. Identifying turbulent energy distribution in real, rather than Fourier, space. Phys. Rev. Lett., 95, 214501.Google Scholar
Davis, A., Marshak, A., Wiscombe, W., and Cahalan, R. 1994. Multifractal characterizations of nonstationarity and intermittency in geophysical fields: observed, retrieved, or simulated. Journal of Geophysical Research: Atmospheres, 99(D4), 8055–8072.CrossRefGoogle Scholar
Davis, A. B., Marshak, A. L., and Wiscombe, W. J. 1993. Bi-multifractal analysis and multiaffine modeling of non-stationary geophysical processes, application to turbulence and clouds. Fractals, 1(3), 560–567.CrossRefGoogle Scholar
de Montera, L., Jouini, M., Verrier, S., Thiria, S., and Crepon, M. 2011. Multifractal analysis of oceanic chlorophyll maps remotely sensed from space. Ocean Sci., 7(2), 219–229.CrossRefGoogle Scholar
de Montera, L., Barthès, L., Mallet, C., and Golé, P. 2009. The effect of rain–no rain intermittency on the estimation of the universal multifractals model parameters. J. Hydrometeor., 10(2), 493–506.CrossRefGoogle Scholar
Denman, K., Okubo, A., and Platt, T. 1977. The chlorophyll fluctuation spectrum in the sea. Limnol. Oceanogr., 22(6), 1033–1038.CrossRefGoogle Scholar
Denman, K. L. 1976. Covariability of chlorophyll and temperature in the sea. Deep Sea Res.: Oceanogr. Abstr., 23, 539–550.Google Scholar
Desprez, M. 2000. Physical and biological impact of marine aggregate extraction along the French coast of the Eastern English Channel: short-and long-term post-dredging restoration. ICES Journal of Marine Science: Journal du Conseil, 57(5), 1428–1438.CrossRefGoogle Scholar
Dickey, T. D. 1991. The emergence of concurrent high resolution physical and bio-optical measurements in the upper ocean and their applications. Rev. Geophys., 29, 383–413.CrossRefGoogle Scholar
Dubrulle, B. 1994. Intermittency in fully developed turbulence: Log-Poisson statistics and generalized scale covariance. Phys. Rev. Lett., 73(7), 959–962.CrossRefGoogle ScholarPubMed
Dur, G., Schmitt, F. G., and Souissi, S. 2007. Analysis of high frequency temperature time series in the Seine estuary from the Marel autonomous monitoring buoy. Hydrobiologia, 588(1), 59–68.CrossRefGoogle Scholar
Echeverria, J. C., Crowe, J. A., Woolfson, M. S., and Hayes-Gill, B. R. 2001. Application of empirical mode decomposition to heart rate variability analysis. Med. Biol. Eng. Comput., 39(4), 471–479.CrossRefGoogle ScholarPubMed
Eggers, J., and Grossmann, S. 1992. Effect of dissipation fluctuations on anomalous velocity scaling in turbulence. Phys. Rev. A, 45(4), 2360.CrossRefGoogle ScholarPubMed
Egolf, P.W., and Weiss, D. A. 1998. Difference-quotient turbulence model: the axisymmetric isothermal jet. Phys. Rev. E, 58(1), 459.CrossRefGoogle Scholar
Embrechts, P., and Maejima, M. 2002. Self-similar processes. Princeton University Press.Google Scholar
Falkovich, G., and Lebedev, V. 1994. Universal direct cascade in two-dimensional turbulence. Phys. Rev. E, 50(5), 3883.CrossRefGoogle ScholarPubMed
Falkovich, G., and Lebedev, V. 2011. Vorticity statistics in the direct cascade of twodimensional turbulence. Phys. Rev. E, 83(4), 045301.CrossRefGoogle Scholar
Falkovich, G., and Sreenivasan, K. R. 2006. Lessons from hydrodynamic turbulence. Phys. Today, 59, 43.CrossRefGoogle Scholar
Falkovich, G., Gawedzki, K., and Vergassola, M. 2001. Particles and fields in fluid turbulence. Rev. Mod. Phys., 73(4).CrossRefGoogle Scholar
Falkovich, G., Xu, H. T., Pumir, A., Bodenschatz, E., Biferale, L., Boffetta, G., Lanotte, A.S., and Toschi, F. 2012. On Lagrangian single-particle statistics. Phys. Fluids, 24(4), 055102.CrossRefGoogle Scholar
Farge, M. 1992. Wavelet transforms and their applications to turbulence. Annu. Rev. Fluid Mech., 24(1), 395–457.CrossRefGoogle Scholar
Farge, M., Kevlahan, N., Perrier, V., and Goirand, E. 1996. Wavelets and turbulence. Proc. IEEE, 84(4), 639–669.CrossRefGoogle Scholar
Feller, W. 1971. An introduction to probalitity theory and its applications. NewYork:Wiley.Google Scholar
Flandrin, P. 1998. Time-frequency/time-scale analysis. San Diego, CA: Academic Press.Google Scholar
Flandrin, P., and Gonçalvès, P. 2004. Empirical mode decompositions as data-driven wavelet-like expansions. IJWMIP, 2(4), 477–496.Google Scholar
Flandrin, P., Rilling, G., and Gonçalvès, P. 2004. Empirical mode decomposition as a filter bank. IEEE Signal Processing Lett., 11(2), 112–114.CrossRefGoogle Scholar
Frisch, U. 1995. Turbulence: the legacy of AN Kolmogorov. Cambridge University Press.CrossRefGoogle Scholar
Frisch, U., and Matsumoto, T. 2002. On multifractality and fractional derivatives. J. Stat. Phys., 108(5-6), 1181–1202.CrossRefGoogle Scholar
Frisch, U., Sulem, P. L., and Nelkin, M. 1978. A simple dynamical model of intermittent fully developed turbulence. J. Fluid Mech., 87(4), 719–736.CrossRefGoogle Scholar
Gagne, Y. 1980. Contribution à l’étude expérimentale de l'intermittence de la turbulence à petite échelle. PhD thesis.
Garcia, H. E., and Gordon, L. I. 1992. Oxygen solubility in seawater: better fitting equations. Limnol. Oceanogr., 37, 1307–1312.CrossRefGoogle Scholar
Ghashghaie, S., Breymann, W., Peinke, J., Talkner, P., and Dodge, Y. 1996. Turbulent cascades in foreign exchange markets. Nature, 381(6585), 767–770.CrossRefGoogle Scholar
Gipe, P. 1995. Wind energy comes of age. Vol. 4. New York: John Wiley & Sons.Google Scholar
Gnedenko, B. V., and Kolmogorov, A. N. 1954. Limit distributions for sums of independent random variables.
Gottschall, Julia, and Peinke, Joachim. 2008. How to improve the estimation of power curves for wind turbines. Environ. Res. Lett., 3(1), 015005.CrossRefGoogle Scholar
Grant, H. L., Stewart, R.W., and Moilliet, A. 1962. Turbulence spectra from a tidal channel. J. Fluid Mech., 12(2), 241–268.CrossRefGoogle Scholar
Grassberger, P., and Procaccia, I. 1983. Generalized dimensions of strange attractors. Phys. Rev. Lett., 50(6), 346.CrossRefGoogle Scholar
Grossmann, S., and Lohse, D. 2004. Fluctuations in turbulent Rayleigh–Bénard convection: the role of plumes. Phys. Fluids, 16, 4462.CrossRefGoogle Scholar
Gurvich, A. S. 1960. Frequency spectra and distribution functions of vertical wind components. Izvestia ANSSSR Geophys Ser, 7, 1042.Google Scholar
Gurvich, A. S., and Yaglom, A.M. 1967. Breakdown of eddies and probability distributions for small-scale turbulence. Phys. Fluids, 10(9), S59–S65.CrossRefGoogle Scholar
Gurvich, A. S., and Zubkovskii, S. L. 1963. Experimental estimate of fluctuations in the turbulent energy dissipation. Izv. Akad. Nauk SSSR, Ser. Geofiz, 12, 1856–1858.Google Scholar
Haar, A. 1910. On the theory of orthogonal function systems. Mathematische Annalen, 69, 331–371.CrossRefGoogle Scholar
Halsey, T. C., Jensen, M. H., Kadanoff, L. P., Procaccia, I., and Shraiman, B. I. 1986. Fractal measures and their singularities: the characterization of strange sets. Phys. Rev. A, 33(2), 1141–1151.CrossRefGoogle ScholarPubMed
Hartlep, T., Tilgner, A., and Busse, F. H. 2003. Large scale structures in Rayleigh-Bénard convection at high Rayleigh numbers. Phys. Rev. Lett., 91(6), 64501.CrossRefGoogle ScholarPubMed
He, G. W. 2011. Anomalous scaling for Lagrangian velocity structure functions in fully developed turbulence. Phys. Rev. E, 83(2), 025301.CrossRefGoogle ScholarPubMed
He, G. W., and Zhang, J. B. 2006. Elliptic model for space-time correlations in turbulent shear flows. Phys. Rev. E, 73, 055303(R).CrossRefGoogle ScholarPubMed
He, X. Z., and Tong, P. 2011. Kraichnan's random sweeping hypothesis in homogeneous turbulent convection. Phys. Rev. E, 83, 037302.CrossRefGoogle ScholarPubMed
He, X. Z., He, G.W., and Tong, P. 2010. Small-scale turbulent fluctuations beyond Taylor's frozen-flow hypothesis. Phys. Rev. E, 81, 065303(R).CrossRefGoogle ScholarPubMed
He, X. Z., Funfschilling, D., Nobach, H., Bodenschatz, E., and Ahlers, G. 2012. Transition to the ultimate state of turbulent Rayleigh-Bénard convection. Phys. Rev. Lett., 108(2), 024502.CrossRefGoogle ScholarPubMed
Heneghan, C., and McDarby, G. 2000. Establishing the relation between detrended fluctuation analysis and power spectral density analysis for stochastic processes. Phys. Rev. E, 62(5), 6103–6110.CrossRefGoogle ScholarPubMed
Hentschel, H. G. E., and Procaccia, I. 1983. The infinite number of generalized dimensions of fractals and strange attractors. Physica D, 8(3), 435–444.CrossRefGoogle Scholar
Hinze, J. O., Sonnenberg, R. E., and Builtjes, P. J. H. 1974. Memory effect in a turbulent boundary-layer flow due to a relatively strong axial variation of the mean-velocity gradient. Appl. Sci. Res., 29(1), 1–13.CrossRefGoogle Scholar
Hu, K., Ivanov, P. C., Chen, Z., Carpena, P., and Stanley, H. E. 2001. Effect of trends on detrended fluctuation analysis. Phys. Rev. E, 64(1), 11114.CrossRefGoogle ScholarPubMed
Huang, N. E. 2005. Hilbert-Huang transform and its applications. World Scientific. Chap. 1. Introduction to the Hilbert-Huang transform and its related mathematical problems, 1–26.
Huang, N. E., and Wu, Z. 2005. An adaptive data analysis method for nonlinear and nonstationary time series: the empirical mode decomposition and Hilbert spectrum analysis. Proceedings of the 4th International Conference on Wavelet and Its Application, Macao.
Huang, N. E., Wu, M. L., Long, S. R., Shen, S. S. P., Qu, W., Gloersen, P., and Fan, K. L. 2003a. A confidence limit for the empirical mode decomposition and Hilbert spectral analysis. Proc. R. Soc. A, 459(2037), 2317–2345.CrossRefGoogle Scholar
Huang, N. E., Wu, M. L., Qu, W., Long, S. R., and Shen, S. S. P. 2003b. Applications of Hilbert-Huang transform to non-stationary financial time series analysis. Appl. Stoch. Model Bus., 19(3), 245–268.CrossRefGoogle Scholar
Huang, N. E., Shen, Z., Long, S. R., Wu, M. C., Shih, H. H., Zheng, Q., Yen, N. C., Tung, C. C., and Liu, H. H. 1998. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc. R. Soc. A, 454(1971), 903–995.CrossRefGoogle Scholar
Huang, N. E., Shen, Z., and Long, S. R. 1999. A new view of nonlinear water waves: the Hilbert spectrum. Annu. Rev. Fluid Mech., 31(1), 417–457.CrossRefGoogle Scholar
Huang, Y. X. 2009. Arbitrary-order Hilbert spectral analysis: definition and application to fully developed turbulence and environmental time series. PhD thesis, Université des Sciences et Technologies de Lille - Lille 1, France & Shanghai University, China.Google Scholar
Huang, Y. X. 2014. Detrended structure-function in fully developed turbulence. J. Turbul., 15(4), 209–220.CrossRefGoogle Scholar
Huang, Y. X., Schmitt, F. G., Lu, Z. M, and Liu, Y. L. 2008a. An amplitude-frequency study of turbulent scaling intermittency using Hilbert spectral analysis. Europhys. Lett., 84, 40010.CrossRefGoogle Scholar
Huang, Y. X., Schmitt, F. G., Lu, Z. M., and Liu, Y. L. 2008b. Analyse de l'invariance d’échelle de séries temporelles par la décomposition modale empirique et l'analyse spectrale de Hilbert. Traitement du Signal, 25, 481–492.Google Scholar
Huang, Y. X., Schmitt, F. G., Lu, Z. M., and Liu, Y. L. 2009a. Analysis of Daily River Flow Fluctuations Using Empirical Mode Decomposition and Arbitrary Order Hilbert Spectral Analysis. J. Hydrol., 373, 103–111.CrossRefGoogle Scholar
Huang, Y. X., Schmitt, F. G., Lu, Z. M., and Liu, Y. L. 2009b. Autocorrelation function of velocity increments in fully developed turbulence. EPL, 86, 40010.CrossRefGoogle Scholar
Huang, Y. X., Schmitt, F. G., Lu, Z. M., Fougairolles, P., Gagne, Y., and Liu, Y. L. 2010. Second-order structure function in fully developed turbulence. Phys. Rev. E, 82(2), 026319.CrossRefGoogle ScholarPubMed
Huang, Y. X., Schmitt, F. G., Hermand, J.-P., Gagne, Y., Lu, Z. M., and Liu, Y. L. 2011a. Arbitrary-order Hilbert spectral analysis for time series possessing scaling statistics: comparison study with detrended fluctuation analysis and wavelet leaders. Phys. Rev. E, 84(1), 016208.CrossRefGoogle ScholarPubMed
Huang, Y. X., Schmitt, F. G., Zhou, Q., Qiu, X., Shang, X. D., Lu, Z. M., and Liu, Y. L. 2011b. Scaling of maximum probability density functions of velocity and temperature increments in turbulent systems. Phys. Fluids, 23, 125101.Google Scholar
Huang, Y. X., Biferale, L., Calzavarini, E., Sun, C., and Toschi, F. 2013. Lagrangian single particle turbulent statistics through the Hilbert-Huang transforms. Phys. Rev. E, 87, 041003(R).CrossRefGoogle Scholar
Huang, Y. X., Schmitt, F. G., and Gagne, Y. 2014. Two-scale correlation and energy cascade in three-dimensional turbulent flows. J. Stat. Mech, 5, P05002.Google Scholar
Hwang, P. A., Huang, N. E., and Wang, D. W. 2003. A note on analyzing nonlinear and nonstationary ocean wave data. Appl. Ocean Res., 25(4), 187–193.CrossRefGoogle Scholar
Inoue, E. 1952. Turbulent fluctuations in temperature in the atmosphere and oceans. J. Meteor. Soc. Japan, 29, 246–253.Google Scholar
Irion, R. 1999. Soap films reveal whirling worlds of turbulence. Science, 284(5420), 1609–1610.CrossRefGoogle Scholar
Jaffard, S. 1999. The multifractal nature of Lévy processes. Probab. Theory Related Fields, 114(2), 207–227.CrossRefGoogle Scholar
Jaffard, S., Lashermes, B., and Abry, P. 2007. Wavelet leaders in multifractal analysis. In Wavelet analysis and applications. Birkhauser Verlag, Basel: Springer, 201–246.Google Scholar
Janicki, A., and Weron, A. 1994. Simulation and chaotic behavior of alpha-stable stochastic processes. New York: Marcel Dekker.Google Scholar
Jánosi, I. M., and Müller, R. 2005. Empirical mode decomposition and correlation properties of long daily ozone records. Phys. Rev. E, 71(5), 56126.CrossRefGoogle ScholarPubMed
Juneja, A., Lathrop, D. P., Sreenivasan, K. R., and Stolovitzky, G. 1994. Synthetic turbulence. Phys. Rev. E, 49(6), 5179.CrossRefGoogle ScholarPubMed
Kader, B. A., and Yaglom, A. M. 1984. Turbulent structure of an unstable atmospheric surface layer. In Nonlinear and Turbulent Processes in Physics, vol. 1, 829.Google Scholar
Kahane, J. P. 1985. Sur le chaos multiplicatif. Ann. Sci. Math. Québec, 9(2), 105–150.Google Scholar
Kang, H., Chester, S., and Meneveau, C. 2003. Decaying turbulence in an active-gridgenerated flow and comparisons with large-eddy simulation. J. Fluid Mech., 480, 129–160.CrossRefGoogle Scholar
Kantelhardt, J. W., Zschiegner, S. A., Koscielny-Bunde, E., Havlin, S., Bunde, A., and Stanley, H. E. 2002. Multifractal detrended fluctuation analysis of nonstationary time series. Physica A, 316(1-4), 87–114.CrossRefGoogle Scholar
Katul, G., and Chu, C.-R. 1998. A theoretical and experimental investigation of energycontaining scales in the dynamic sublayer of boundary-layer flows. Boundary-Layer Meteorol., 86(2), 279–312.CrossRefGoogle Scholar
Katul, G. G., Chu, C. R., Parlange, M. B., Albertson, J. D., and Ortenburger, T. A. 1995. Low-wavenumber spectral characteristics of velocity and temperature in the atmospheric surface layer. J. Geophys. Res., 100(D7), 14243–14255.CrossRefGoogle Scholar
Katul, G. G., Porporato, A., and Nikora, V. 2012. Existence of k- 1 power-law scaling in the equilibrium regions of wall-bounded turbulence explained by Heisenberg's eddy viscosity. Phys. Rev. E, 86(6), 066311.CrossRefGoogle ScholarPubMed
Katzenstein, W., Fertig, E., and Apt, J. 2010. The variability of interconnected wind plants. Energy Policy, 38(8), 4400–4410.CrossRefGoogle Scholar
Kellay, H., Wu, X. L., and Goldburg, W. I. 1998. Vorticity measurements in turbulent soap films. Phys. Rev. Lett., 80(2), 277–280.CrossRefGoogle Scholar
Kellay, H., and Goldburg, W. I. 2002. Two-dimensional turbulence: a review of some recent experiments. Rep. Prog. Phys., 65(5), 845.CrossRefGoogle Scholar
Kelley, D. H., and Ouellette, N. T. 2011. Spatiotemporal persistence of spectral fluxes in two-dimensional weak turbulence. Phys. Fluids, 23(11), 115101.CrossRefGoogle Scholar
Khurana, N., and Ouellette, N. T. 2012. Interactions between active particles and dynamical structures in chaotic flow. Phys. Fluids, 24(9), 091902.CrossRefGoogle Scholar
Kida, S. 1991. Log stable distribution and intermittency of turbulence. J. Phys. Soc. Jpn., 60(1), 5–8.CrossRefGoogle Scholar
Kolmogorov, A. N. 1940. The Wiener spiral and some other interesting curves in Hilbert space. Dokl. Akad. Nauk SSSR, 26(2), 115–118.Google Scholar
Kolmogorov, A. N. 1941a. Energy dissipation in locally isotropic turbulence. Doklady AN SSSR, 32(1), 19–21.Google Scholar
Kolmogorov, A. N. 1941b. Local structure of turbulence in an incompressible fluid at very high Reynolds numbers. Dokl. Akad. Nauk SSSR, 30, 301.Google Scholar
Kolmogorov, A. N. 1962. A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number. J. Fluid Mech., 13, 82–85.CrossRefGoogle Scholar
Korotenko, K. A., Sentchev, A. V., and Schmitt, F. G. 2012. Effect of variable winds on current structure and Reynolds stresses in a tidal flow: analysis of experimental data in the eastern English Channel. Ocean Science, 8(6), 1025–1040.CrossRefGoogle Scholar
Koscielny-Bunde, E., Kantelhardt, J. W., Braun, P., Bunde, A., and Havlin, S. 2006. Longterm persistence and multifractality of river runoff records: detrended fluctuation studies. J. Hydrol., 322(1-4), 120–137.CrossRefGoogle Scholar
Kraichnan, R. H. 1967. Inertial Ranges in Two-Dimensional Turbulence. Phys. Fluids, 10, 1417–1423.CrossRefGoogle Scholar
Kraichnan, R. H., and Montgomery, D. 1980. Two-dimensional turbulence. Rep. Prog. Phys., 43, 547.CrossRefGoogle Scholar
Kunnen, R. P. J., Clercx, H. J. H., Geurts, B. J., van Bokhoven, L. J. A., Akkermans, R. A. D., and Verzicco, R. 2008. Numerical and experimental investigation of structure-function scaling in turbulent Rayleigh-Bénard convection. Phys. Rev. E, 77(1), 016302.CrossRefGoogle ScholarPubMed
Kuramoto, Y., Battogtokh, D., and Nakao, H. 1998. Multiaffine chemical turbulence. Phys. Rev. Lett., 81(16), 3543.CrossRefGoogle Scholar
Landau, L. D., and Lifshits, E. M. 1944. Fluid mechanics, 1st Russian edn. Landberg, L. 1999. Short-term prediction of the power production from wind farms. J.Wind Eng. Ind. Aerodyn., 80(1), 207–220.
Lashermes, B., Abry, P., and Chainais, P. 2004. New insights into the estimation of scaling exponents. IWMIP, 2(04), 497–523.Google Scholar
Lashermes, B., Jaffard, S., and Abry, P. 2005. Wavelet leader based multifractal analysis. In IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005. Proceedings ICASSP'05., vol. 4. IEEE, iv–161.CrossRefGoogle Scholar
Lashermes, B., Roux, S. G., Abry, P., and Jaffard, S. 2008. Comprehensive multifractal analysis of turbulent velocity using the wavelet leaders. Eur. Phys. J. B, 61(2), 201–215.CrossRefGoogle Scholar
Lévy, P. 1937. Théorie de laddition des variables aléatoires. Gauthiers-Villars, Paris.Google Scholar
Li, M. Y., and Huang, Y. X. 2014. Hilbert–Huang Transform based multifractal analysis of China stock market. Physica A, 406, 222–229.CrossRefGoogle Scholar
Loh, C. H., Wu, T. C., and Huang, N. E. 2001. Application of the Empirical Mode Decomposition-Hilbert Spectrum Method to Identify Near-Fault Ground-Motion Characteristics and Structural Responses. BSSA, 91(5), 1339–1357.Google Scholar
Lohse, D., and Xia, K.-Q. 2010. Small-scale properties of turbulent Rayleigh-Bénard convection. Annu. Rev. Fluid Mech., 42, 335–364.CrossRefGoogle Scholar
Long, S. R., Huang, N. E., Tung, C. C., Wu, M. L., Lin, R. Q., Mollo-Christensen, E., and Yuan, Y. 1995. The Hilbert techniques: an alternate approach for non-steady time series analysis. IEEE Geoscience and Remote Sensing Soc. Lett., 3, 6–11.Google Scholar
Loutridis, S. J. 2005. Resonance identification in loudspeaker driver units: A comparison of techniques. Appl. Acoust., 66(12), 1399–1426.CrossRefGoogle Scholar
Lovejoy, S, and Schertzer, D. 2012. Haar wavelets, fluctuations and structure functions: convenient choices for geophysics. Nonlinear Proc. Geoph., 19(5), 513–527.CrossRefGoogle Scholar
Lovejoy, S, Schertzer, D, Tessier, Y, and Gaonac'h, H. 2001a. Multifractals and resolutionindependent remote sensing algorithms: the example of ocean colour. Int. J. Remote Sens., 22(7), 1191–1234.CrossRefGoogle Scholar
Lovejoy, S., Currie, W. J. S., Tessier, Y., Claereboudt, M. R., Bourget, E., Roff, J. C., and Schertzer, D. 2001b. Universal multifractals and ocean patchiness: phytoplankton, physical fields and coastal heterogeneity. J. Plankton Res., 23(2), 117-141.CrossRefGoogle Scholar
Lovejoy, Shaun, and Schertzer, Daniel. 2013. The weather and climate: emergent laws and multifractal cascades. Cambridge University Press.CrossRefGoogle Scholar
Ludena, Carenne. 2008. Lp-variations for multifractal fractional random walks. Ann. Appl. Probab., 18(3), 1138-1163.CrossRefGoogle Scholar
Lumley, J. L. 1970. Toward a turbulent constitutive relation. J. Fluid Mech., 41(02), 413-434.CrossRefGoogle Scholar
Maejima, M. 1983. On a class of self-similar processes. Probab. Theory Related Fields, 62(2), 235-245.Google Scholar
Malik, S. C., and Arora, S. 1992. Mathematical Analysis. New York: John Wiley & Sons Inc.Google Scholar
Mallat, S., and Hwang, W. L. 1992. Singularity detection and processing with wavelets. IEEE Trans. Inform. Theory, 38(2), 617-643.CrossRefGoogle Scholar
Mallat, S. G. 1999. A wavelet tour of signal processing. Burlington: Academic Press.Google Scholar
Mandelbrot, B. B. 1974. Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier. J. Fluid Mech., 62(2), 331-358.CrossRefGoogle Scholar
Mandelbrot, B. B. 1983. The fractal geometry of nature/Revised and enlarged edition. Vol. 1.Google Scholar
Mandelbrot, B. B. 1991. Random multifractals: negative dimensions and the resulting limitations of the thermodynamic formalism. Proc. R. Soc. A, 434(1890), 79-88.CrossRefGoogle Scholar
Mandelbrot, B. B., Fisher, A. J., and Calvet, L. E. 1997. A Multifractal Model of Assets Returns. Cowles Foundation discussion paper no. 1164.
Mandelbrot, B. B., and Van Ness, J.W. 1968. Fractional Brownian Motions, Fractional Noises and Applications. SIAM Review, 10, 422.CrossRefGoogle Scholar
Manneville, Paul. 2004. Instabilités, chaos et turbulence. Editions Ecole Polytechnique.
Mantegna, R. N., and Stanley, H. E. 1996. Turbulence and financial markets. Nature, 383(6601), 587-588.CrossRefGoogle Scholar
Marsan, D., Schertzer, D., and Lovejoy, S. 1996. Causal space-time multifractal processes: Predictability and forecasting of rain fields. Journal of Geophysical Research: Atmospheres, 101(D21), 26333-26346.CrossRefGoogle Scholar
Meneveau, C. 2011. Lagrangian dynamics and models of the velocity gradient tensor in turbulent flows. Annu. Rev. Fluid Mech., 43, 219-245.CrossRefGoogle Scholar
Meneveau, C., and Sreenivasan, K. R. 1987. Simple multifractal cascade model for fully developed turbulence. Phys. Rev. Lett., 59(13), 1424.CrossRefGoogle ScholarPubMed
Merrifield, S. T., Kelley, D. H., and Ouellette, N. T. 2010. Scale-dependent statistical geometry in two-dimensional flow. Phys. Rev. Lett., 104(25), 254501.CrossRefGoogle ScholarPubMed
Meyer, Yves. 1995. Wavelets and operators. Vol. 1. Cambridge: Cambridge University Press.Google Scholar
Milan, P., Wächter, M., and Peinke, J. 2013. Turbulent character of wind energy. Phys. Rev. Lett., 110(13), 138701.CrossRefGoogle ScholarPubMed
Molla, K. I., Rahman, M. S., Sumi, A., and Banik, P. 2006. Empirical mode decomposition analysis of climate changes with special reference to rainfall data. Discrete Dyn. Nat. Soc., 45348.CrossRefGoogle Scholar
Monin, A. S., and Yaglom, A. M. 1971. Statistical Fluid Mechanics vd II. MIT Press.Google Scholar
Morales, A, Wächter, M, and Peinke, J. 2012. Characterization of wind turbulence by higher-order statistics. Wind Energy, 15(3), 391-406.
Mordant, N., Delour, J., Léveque, E., Arnéodo, A., and Pinton, J.-F. 2002. Long time correlations in Lagrangian dynamics: a key to intermittency in turbulence. Phys. Rev. Lett., 89(25), 254502.CrossRefGoogle ScholarPubMed
Muzy, J. F., Bacry, E., and Arneodo, A. 1991. Wavelets and multifractal formalism for singular signals: application to turbulence data. Phys. Rev. Lett., 67(25), 3515-3518.CrossRefGoogle ScholarPubMed
Muzy, J. F., Bacry, E., and Arneodo, A. 1993. Multifractal formalism for fractal signals: the structure-function approach versus the wavelet-transform modulus-maxima method. Phys. Rev. E, 47(2), 875-884.CrossRefGoogle ScholarPubMed
Muzy, J.-F., Bacry, E., and Kozhemyak, A. 2006. Extreme values and fat tails of multifractal fluctuations. Phys. Rev. E, 73(6), 066114.CrossRefGoogle ScholarPubMed
Muzy, J.-F., and Bacry, E. 2002. Multifractal stationary random measures and multifractal random walks with log infinitely divisible scaling laws. Phys. Rev. E, 66(5), 056121.CrossRefGoogle ScholarPubMed
Nakao, H. 2000. Multi-scaling properties of truncated Lévy flights. Phys. Lett. A, 266(4), 282-289.CrossRefGoogle Scholar
Nam, K., Ott, E., Antonsen Jr, T. M., and Guzdar, P. N. 2000. Lagrangian chaos and the effect of drag on the enstrophy cascade in two-dimensional turbulence. Phys. Rev. Lett., 84(22), 5134-5137.CrossRefGoogle ScholarPubMed
Nam, S., Kim, G., Kim, K. R., Kim, K., Cheng, L. Oh, Kim, K. W., Ossi, H., and Kim, Y. G. 2005. Application of real-time monitoring buoy systems for physical and biogeochemical parameters in the coastal ocean around the Korean peninsula. Mar. Technol. Soc. J., 39(2), 70-80.CrossRefGoogle Scholar
Nickels, T. B. B., Marusic, I., Hafez, S., and Chong, M. S. 2005. Evidence of the k-11 Law in a High-Reynolds-Number Turbulent Boundary Layer. Phys. Rev. Lett., 95(7), 074501.CrossRefGoogle Scholar
Nicolis, G., and Nicolis, C. 2012. Foundations of complex systems: emergence, information and predicition. World Scientific.
Niemela, J. J., Skrbek, L., Sreenivasan, K. R., and Donnelly, R. J. 2000. Turbulent convection at very high Rayleigh numbers. Nature, 404(6780), 837-840.CrossRefGoogle ScholarPubMed
Nieves, V., Llebot, C., Turiel, A., Solé, J.ordi, García-Ladona, E., Estrada, M., and Blasco, D. 2007. Common turbulent signature in sea surface temperature and chlorophyll maps. Geophys. Res. Lett., 34(23).CrossRefGoogle Scholar
Nikias, C. L, and Shao, M. 1995. Signal processing with alpha-stable distributions and applications. Wiley-Interscience.Google Scholar
Nikora, V. 1999. Origin of the -1 spectral law in wall-bounded turbulence. Phys. Rev. Lett., 83(4), 734.CrossRefGoogle Scholar
Novikov, E. A. 1969. Scale similarity for random fields. Soviet Physics Doklady, 14, 104-107.Google Scholar
Novikov, E. A. 1971. Intermittency and scale similarity in the structure of a turbulent flow. J. Appl. Math. Mech., 35(2), 231-241.CrossRefGoogle Scholar
Novikov, E. A. 1989. Two-particle description of turbulence, Markov property, and intermittency. Phys. Fluids A, 1(2), 326-330.CrossRefGoogle Scholar
Novikov, E. A. 1990. The effects of intermittency on statistical characteristics of turbulence and scale similarity of breakdown coefficients. Phys. Fluids A, 2(5), 814-820.CrossRefGoogle Scholar
Novikov, E. A. 1994. Infinitely divisible distributions in turbulence. Phys. Rev. E, 50(5), R3303.CrossRefGoogle ScholarPubMed
Novikov, E. A., and Stewart, R.W. 1964. The intermittency of turbulence and the spectrum of energy dissipation fluctuations. Bull. Acad. Sci. SSSR Geophy. Ser., 3, 408-413.Google Scholar
Obukhov, A. M. 1941. Spectral energy distribution in a turbulent flow. Dokl. Akad. Nauk SSSR, 32, 22-24.Google Scholar
Obukhov, A. M. 1949. Structure of the temperature field in a turbulent flow. Izv. Akad. Nauk SSSR Ser. Geog. i Geofiz., 13, 58-69.Google Scholar
Obukhov, A. M. 1959. On the influence of Archimedean forces on the structure of the temperature field in a turbulent flow. Doklady Akademi Nauk SSSR, 125, 1246–48.Google Scholar
Obukhov, A. M. 1962. Some specific features of atmospheric turbulence. J. Fluid Mech., 13(1), 77–81.Google Scholar
Oświȩcimka, P., Kwapień, J., and Drożdż, S. 2006. Wavelet versus detrended fluctuation analysis of multifractal structures. Phys. Rev. E, 74(1), 16103.CrossRefGoogle ScholarPubMed
Panchev, S. 1972. Random Functions and Turbulence. Oxford: Pergamon.Google Scholar
Paret, J., Jullien, M.C., and Tabeling, P. 1999. Vorticity statistics in the two-dimensional enstrophy cascade. Phys. Rev. Lett., 83(17), 3418–3421.CrossRefGoogle Scholar
Parisi, G., and Frisch, U. 1985. On the singularity spectrum of fully developed turbulence. in M., Ghil, R., Benzi, G., Parisi (eds.), Turbulence and Predictability in Geophysical Fluid Dynamics and Climatic Dynamics, Amsterdam: North-Holland, 84–87.Google Scholar
Pecknold, S., Lovejoy, S., Schertzer, D., Hooge, C., and Malouin, J. F. 1993. The simulation of universal multifractals. In Perdang, J. M., and A., Lejeune (eds), Cellular Automata: Prospects in astrophysical applications, vol. 1. World Scientific, 228–267.Google Scholar
Peinke, J., Barth, S., Boettcher, F., Heinemann, D., and Lange, B. 2004. Turbulence, a challenging problem for wind energy. Physica A, 338(1), 187–193.CrossRefGoogle Scholar
Peng, C. K., Buldyrev, S. V., Havlin, S., Simons, M., Stanley, H. E., and Goldberger, A. L. 1994. Mosaic organization of DNA nucleotides. Phys. Rev. E, 49(2), 1685–1689.CrossRefGoogle ScholarPubMed
Percival, D. B., and Walden, A. T. 1993. Spectral Analysis for Physical Applications: Multitaper and Conventional Univariate Techniques. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Perpete, N. 2013. Construction of multifractal fractional randowm walks with Hurst index smaller than 1/2. Stoch. Dyn., 13(4), 1350003.CrossRefGoogle Scholar
Perpete, N., and Schmitt, F. G. 2011. A discrete log-normal process to sequentially generate a multifractal time series. J. Stat. Mech., 2011(12), P12013.CrossRefGoogle Scholar
Perry, A. E., Henbest, S., and Chong, M. S. 1986. A theoretical and experimental study of wall turbulence. J. Fluid Mech., 165, 163–199.CrossRefGoogle Scholar
Pipiras, V., and Taqqu, M. S. 2000. Integration questions related to fractional Brownian motion. Probab. Theory Related Fields, 118(2), 251–291.CrossRefGoogle Scholar
Piquet, J. 1999. Turbulent flows: models and physics. Berlin: Springer.CrossRefGoogle Scholar
Platt, T., and Denman, K. L. 1975. Spectral analysis in ecology. Annu. Rev. Ecol. Syst., 189–210.Google Scholar
Pond, S., and Stewart, R. W. 1965. Measurements of the statistical characteristics of smallscale turbulent motions. Izv. Atmos. Oceanic Phys, 1, 914–919.Google Scholar
Ponomarenko, V. I., Prokhorov, M. D., Bespyatov, A. B., Bodrov, M. B., and Gridnev, V. I. 2005. Deriving main rhythms of the human cardiovascular system from the heartbeat time series and detecting their synchronization. Chaos Soliton Fract., 23, 1429–1438.CrossRefGoogle Scholar
Pope, S. B. 2000. Turbulent Flows. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Pottier, C., Turiel, A., and Garçon, V. 2008. Inferring missing data in satellite chlorophyll maps using turbulent cascading. Remote Sens. Environ., 112(12), 4242–4260.CrossRefGoogle Scholar
Pugh, D. 2004. Changing sea levels: effects of tides, weather and climate. Cambridge: Cambridge University Press.Google Scholar
Qiu, X., Mompean, G., Schmitt, F. G., and Thompson, R. L. 2011. Modeling turbulentbounded flow using non-Newtonian viscometric functions. J. Turbul 12(15), 1–18.CrossRefGoogle Scholar
Qiu, X., Huang, Y. X., Zhou, Q., and Sun, C. 2014. Scaling of maximum probability density function of velocity increments in turbulent Rayleigh-Bénard convection. J. Hydrodyn., 26(3), 351–362.CrossRefGoogle Scholar
Rajput, B. S., and Rosinski, J. 1989. Spectral representations of infinitely divisible processes. Probab. Theory Related Fields, 82(3), 451–487.CrossRefGoogle Scholar
Renosh, P. R., Schmitt, F. G., Loisel, H., Sentchev, A., and Mériaux, X. 2014. High frequency variability of particle size distribution and its dependency on turbulence over the sea bottom during re-suspension processes. Cont. Shelf Res., 77, 51–60.CrossRefGoogle Scholar
Renosh, P. R., Schmitt, F. G., and Loisel, H. 2015. Scaling analysis of ocean surface turbulent heterogeneities from satellite remote sensing: use of 2D structure functions. PLoS One, 10(5), e0126975.CrossRefGoogle ScholarPubMed
Rhodes, R., and Vargas, V. 2014. Gaussian multiplicative chaos and applications: a review. Probability Surveys, 11, 315–392.CrossRefGoogle Scholar
Richardson, L. F. 1922. Weather prediction by numerical process. Cambridge: Cambridge University Press.Google Scholar
Rilling, G., Flandrin, P., and Gonçalvès, P. 2003. On empirical mode decomposition and its algorithms. IEEE-EURASIP Workshop on Nonlinear Signal and Image Processing, 3, 8–11.Google Scholar
Robert, R., and Vargas, V. 2010. Gaussian multiplicative chaos revisited. Ann. Probab., 38(2), 605–631.CrossRefGoogle Scholar
Rodrigues Neto, C., Zanandrea, A., Ramos, F. M., Rosa, R. R., Bolzan, M. J. A., and , L. D. A. 2001. Multiscale analysis from turbulent time series with wavelet transform. Physica A, 295(1-2), 215–218.CrossRefGoogle Scholar
Sadegh Movahed, M., Jafari, G. R., Ghasemi, F., Rahvar, S., and Rahimi Tabar, M. R. 2006. Multifractal detrended fluctuation analysis of sunspot time series. J. Stat. Mech., 02003.Google Scholar
Saito, Y. 1992. Log-gamma distribution model of intermittency in turbulence. J. Phys. Soc. Jpn., 61(2), 403–406.CrossRefGoogle Scholar
Samorodnitsky, G., and Taqqu, M. S. 1994. Stable non-Gaussian random processes: stochastic models with infinite variance. Chapman & Hall.Google Scholar
Sanchez, I. 2006. Short-term prediction of wind energy production. Int. J. Forecasting, 22(1), 43–56.CrossRefGoogle Scholar
Sawford, B. L., and Yeung, P. K. 2011. Kolmogorov similarity scaling for one-particle Lagrangian statistics. Phys. Fluids, 23, 091704.CrossRefGoogle Scholar
Schertzer, D., and Lovejoy, S. 1984. On the dimension of atmospheric motions. 505–512.Google Scholar
Schertzer, D., and Lovejoy, S. 1987. Physical modeling and analysis of rain and clouds by anisotropic scaling multiplicative processes. J. Geophys. Res, 92(D8), 9693–9714.CrossRefGoogle Scholar
Schertzer, D., and Lovejoy, S. 1992. Hard and soft multifractal processes. Physica A, 185(1), 187–194.CrossRefGoogle Scholar
Schertzer, D., Lovejoy, S., and Schmitt, F. G. 1995. Structures in turbulence and multifractal universality. in M., Meneguzzi, A., Pouquet and P. L., Sulem (eds.), Small-scale structures in 3D hydro and MHD turbulence. Berlin: Springer Verlag, 137–144.Google Scholar
Schertzer, D., Lovejoy, S., Schmitt, F. G., Chigirinskaya, Y., and Marsan, D. 1997. Multifractal cascade dynamics and turbulent intermittency. Fractals, 5(3), 427–471.CrossRefGoogle Scholar
Schmitt, F., Schertzer, D., Lovejoy, S., Brunet, Y., et al. 1994. Empirical study of multifractal phase transitions in atmospheric turbulence. Nonlinear Proc. Geoph., 1(2/3), 95–104.CrossRefGoogle Scholar
Schmitt, F., Schertzer, D., Lovejoy, S., and Brunet, Y. 1996. Multifractal temperature and flux of temperature variance in fully developed turbulence. Europhys. Lett., 34(3), 195.CrossRefGoogle Scholar
Schmitt, F. G. 2007a. About Boussinesq's turbulent viscosity hypothesis: historical remarks and a direct evaluation of its validity. C.R. Mécanique, 335(9), 617–627.CrossRefGoogle Scholar
Schmitt, F. G. 2007b. Direct test of a nonlinear constitutive equation for simple turbulent shear flows using DNS data. Commun. Nonlinear Sci. Numer. Simul., 12(7), 1251–1264.CrossRefGoogle Scholar
Schmitt, F. G., and Chainais, P. 2007. On causal stochastic equations for log-stable multiplicative cascades. Eur. Phys. J. B, 58(2), 149–158.CrossRefGoogle Scholar
Schmitt, F. G., and Seuront, L. 2001. Multifractal random walk in copepod behavior. Physica A, 301(1-4), 375–396.CrossRefGoogle Scholar
Schmitt, F. G., Lavallee, D., Schertzer, D., and Lovejoy, S. 1992. Empirical determination of universal multifractal exponents in turbulent velocity fields. Phys. Rev. Lett., 68(3), 305–308.CrossRefGoogle ScholarPubMed
Schmitt, F. G., Schertzer, D., and Lovejoy, S. 1999. Multifractal analysis of foreign exchange data. Appl. Stoch. Mod. Data Anal., 15(1), 29–53.Google Scholar
Schmitt, F. G., Huang, Y. X., Lu, Z., Zongo, S. B., Molinero, J. C., and Liu, Y. 2007. Analysis of nonliner biophysical time series in aquatic environments: scaling properties and empirical mode decomposition. In Tsonis, A., and Elsner, J. (eds.), Nonlinear Dynamics in Geosciences. Springer, 261–280.Google Scholar
Schmitt, F. G., Dur, G., Souissi, S., and Brizard Zongo, S. 2008. Statistical properties of turbidity, oxygen and pH fluctuations in the Seine river estuary (France). Physica A, 387(26), 6613–6623.CrossRefGoogle Scholar
Schmitt, F. G., Vinkovic, I., and Buffat, M. 2010. Use of Lagrangian statistics for the analysis of the scale separation hypothesis in turbulent channel flow. Phys. Lett. A, 374(33), 3319–3327.CrossRefGoogle Scholar
Schmitt, F. G. 2005. Relating Lagrangian passive scalar scaling exponents to Eulerian scaling exponents in turbulence. EPJ B, 48(1), 129–137.Google Scholar
Schmitt, F. G. 2006. Linking Eulerian and Lagrangian structure functions scaling exponents in turbulence. Physica A, 368(2), 377–386.CrossRefGoogle Scholar
Schmitt, F. G., and Marsan, D. 2001. Stochastic equations generating continuous multiplicative cascades. EPJ B, 20(1), 3–6.Google Scholar
Schmitt, F. G., Huang, Y. X., Lu, Z. M., Liu, Y. L., and Fernandez, N. 2009. Analysis of velocity fluctuations and their intermittency properties in the surf zone using empirical mode decomposition. J. Mar. Syst., 77, 473–481.CrossRefGoogle Scholar
Serrano, E., and Figliola, A. 2009. Wavelet leaders: a new method to estimate the multifractal singularity spectra. Physica A, 388(14), 2793–2805.CrossRefGoogle Scholar
Seuront, L., and Schmitt, F. G. 2005. Multiscaling statistical procedures for the exploration of biophysical couplings in intermittent turbulence. Part I. Theory. Deep Sea Res. Part II, 52(9-10), 1308–1324.Google Scholar
Seuront, L., Schmitt, F., Lagadeuc, Y., Schertzer, D., Lovejoy, S., and Frontier, S. 1996a. Multifractal analysis of phytoplankton biomass and temperature in the ocean. Geophys. Res. Lett., 23(24), 3591–3594.CrossRefGoogle Scholar
Seuront, L., Schmitt, F., Schertzer, D., Lagadeuc, Y., and Lovejoy, S. 1996b. Multifractal intermittency of Eulerian and Lagrangian turbulence of ocean temperature and plankton fields. Nonlinear Proc. Geoph., 3(4), 236–246.CrossRefGoogle Scholar
Seuront, L., Schmitt, F., Lagadeuc, Y., Schertzer, D., and Lovejoy, S. 1999. Universal multifractal analysis as a tool to characterize multiscale intermittent patterns: example of phytoplankton distribution in turbulent coastal waters. J. Plankton Res., 21(5), 877–922.CrossRefGoogle Scholar
Shang, X. D., Qiu, X.-L., Tong, P., and Xia, K.-Q. 2003. Measured local heat transport in turbulent Rayleigh-Bénard convection. Phys. Rev. Lett., 90, 074501.CrossRefGoogle ScholarPubMed
Shang, X. D., Qiu, X.-L., Tong, P., and Xia, K.-Q. 2004. Measurements of the local convective heat flux in turbulent Rayleigh-Bénard convection. Phys. Rev. E, 70, 026308.CrossRefGoogle ScholarPubMed
Shang, X. D., Tong, P., and Xia, K.-Q. 2008. Scaling of the local convective heat flux in turbulent Rayleigh-Bénard convection. Phys. Rev. Lett., 100(6), 244503.CrossRefGoogle ScholarPubMed
She, Z. S., and Lévêque, E. 1994. Universal scaling laws in fully developed turbulence. Phys. Rev. Lett., 72(3), 336–339.CrossRefGoogle ScholarPubMed
She, Z. S., and Waymire, E. C. 1995. Quantized Energy Cascade and Log-Poisson Statistics in Fully Developed Turbulence. Phys. Rev. Lett., 74(2), 262–265.CrossRefGoogle ScholarPubMed
Shraiman, B. I., and Siggia, E. D. 2000. Scalar turbulence. Nature, 405(6787), 639–646.CrossRefGoogle ScholarPubMed
Siggia, E. D. 1994. High rayleigh number convection. Annu. Rev. Fluid Mech., 26, 137–168.CrossRefGoogle Scholar
Solé, J., Turiel, A., and Llebot, J. E. 2007. Using empirical mode decomposition to correlate paleoclimatic time-series. Nat. Hazard Earth Sys., 7, 299–307.CrossRefGoogle Scholar
Sørensen, P., Hansen, A. D., and Carvalho Rosas, P. A. 2002. Wind models for simulation of power fluctuations from wind farms. J. Wind Eng. Ind. Aerodyn., 90(12), 1381–1402.CrossRefGoogle Scholar
Sreenivasan, K. R. 1991. On Local Isotropy of Passive Scalars in Turbulent Shear Flows. Proc. R. Soc. A, 434(1890), 165–182.CrossRefGoogle Scholar
Sreenivasan, K. R., and Antonia, R. A. 1997. The phenomenology of small-scale turbulence. Annu. Rev. Fluid Mech., 29, 435–472.CrossRefGoogle Scholar
Sreenivasan, K. R., and Kailasnath, P. 1993. An update on the intermittency exponent in turbulence. Phys. Fluids A, 5(2), 512–514.CrossRefGoogle Scholar
Svendsen, I. A. 1987. Analysis of surf zone turbulence. J. Geophys. Res., 92(C5), 5115–5124.CrossRefGoogle Scholar
Tabeling, P. 2002. Two-dimensional turbulence: a physicist approach. Phys. Rep., 362(1), 1–62.CrossRefGoogle Scholar
Tan, H. S., Huang, Y. X., and Meng, J.-P. 2014. Hilbert Statistics of Vorticity Scaling in Two-Dimensional Turbulence. Phys. Fluids, 26(2), 015106.Google Scholar
Taqqu, M. S., and Wolpert, R. L. 1983. Infinite variance self-similar processes subordinate to a Poisson measure. Probab. Theory Related Fields, 62(1), 53–72.Google Scholar
Taqqu, M. S. 1988. Self-similar processes. Encyclopedia of Statistical Sciences.
Taylor, G. I. 1938. The Spectrum of Turbulence. Proc. R. Soc. A, 164(919), 476–490.CrossRefGoogle Scholar
Tennekes, H., and Lumley, J. L. 1972. A First Course in Turbulence. MIT Press.Google Scholar
Tessier, Y, Lovejoy, S., Schertzer, D., Lavallée, D., and Kerman, B. 1993. Universal multifractal indices for the ocean surface at far red wavelengths. Geophys. Res. Lett., 20(12), 1167–1170.CrossRefGoogle Scholar
Tessier, Y., Lovejoy, S., Hubert, P., Schertzer, D., and Pecknold, S. 1996. Multifractal analysis and modeling of rainfall and river flows and scaling, causal transfer functions. J. Geophys. Res., 101, 26427–26440.CrossRefGoogle Scholar
Thomson, W. 1887. On the propagation of laminar motion through a turbulently moving inviscid liquid. Philos. Mag., 342–353.Google Scholar
Toschi, F., and Bodenschatz, E. 2009. Lagrangian properties of particles in turbulence. Annu. Rev. Fluid Mech., 41, 375–404.CrossRefGoogle Scholar
Toschi, F., Biferale, L., Boffetta, G., Celani, A., Devenish, B. J., and Lanotte, A. 2005. Acceleration and vortex filaments in turbulence. J. Turbul., 6(6), 15.CrossRefGoogle Scholar
Tran, T., Chakraborty, P., Guttenberg, N., Prescott, A., Kellay, H., Goldburg, W., Goldenfeld, N., and Gioia, G. 2010. Macroscopic effects of the spectral structure in turbulent flows. Nature Phys., 6(6), 438–441.CrossRefGoogle Scholar
Tsang, Y. K., Ott, E., Antonsen Jr, T. M., and Guzdar, P. N. 2005. Intermittency in twodimensional turbulence with drag. Phys. Rev. E, 71(6), 066313.CrossRefGoogle Scholar
Tsinober, A. 2009. An informal conceptual introduction to turbulence. Dordrecht: Springer Verlag.CrossRefGoogle Scholar
Turiel, A., Nieves, V., García-Ladona, E., Font, J., Rio, M.-H., and Larnicol, G. 2009. The multifractal structure of satellite sea surface temperature maps can be used to obtain global maps of streamlines. Ocean Science, 5(4), 447–460.CrossRefGoogle Scholar
Uchaikin, V. V., and Zolotarev, V. M. 1999. Chance and stability: stable distributions and their applications. Walter de Gruyter.CrossRefGoogle Scholar
Van Heijst, G. J. F., and Clercx, H. J. H. 2009. Laboratory modeling of geophysical vortices. Annu. Rev. Fluid Mech., 41, 143–164.CrossRefGoogle Scholar
Veltcheva, A. D., and Soares, C. G. 2004. Identification of the components of wave spectra by the Hilbert Huang transform method. Appl. Ocean Res., 26(1-2), 1–12.CrossRefGoogle Scholar
Vicsek, T., and Barabasi, A.-L. 1991. Multi-affine model for the velocity distribution in fully turbulent flows. J. Phys. A, 24(15), L845.CrossRefGoogle Scholar
Warhaft, Z. 2000. Passive scalars in turbulent flows. Annu. Rev. Fluid Mech., 32(1), 203–240.CrossRefGoogle Scholar
Weisse, Ralf. 2010. Marine climate and climate change: storms, wind waves and storm surges. Springer Science & Business Media.CrossRefGoogle Scholar
Wendt, H., Abry, P., and Jaffard, S. 2007. Bootstrap for Empirical Multifractal Analysis with Application to Hydrodynamic Turbulences. IEEE Signal Processing Mag., 24(4), 38–48.CrossRefGoogle Scholar
Wilcox, D. C., et al. 1998. Turbulence modeling for CFD. Vol. 2. DCW industries La Canada, CA.Google Scholar
Wu, Z., and Huang, N. E. 2004. A study of the characteristics of white noise using the empirical mode decomposition method. Proc. R. Soc. A, 460, 1597–1611.CrossRefGoogle Scholar
Wu, Z., and Huang, N. E. 2010. On the filtering properties of the empirical mode decomposition. Adv. Adapt. Data Anal., 2(04), 397–414.CrossRefGoogle Scholar
Wu, Z., Huang, N. E., Long, S. R., and Peng, C. K. 2007. On the trend, detrending, and variability of nonlinear and nonstationary time series. PNAS, 104(38), 14889.CrossRefGoogle ScholarPubMed
Xi, H. D., and Xia, K. Q. 2007. Cessations and reversals of the large-scale circulation in turbulent thermal convection. Phys. Rev. E, 75(6), 066307.CrossRefGoogle ScholarPubMed
Xi, H. D., Lam, S., and Xia, K. Q. 2004. From laminar plumes to organized flows: the onset of large-scale circulation in turbulent thermal convection. J. Fluid Mech., 503, 47–56.CrossRefGoogle Scholar
Xia, H., Punzmann, H., Falkovich, G., and Shats, M. G. 2008. Turbulence-condensate interaction in two dimensions. Phys. Rev. Lett., 101(19), 194504.CrossRefGoogle ScholarPubMed
Xia, H., Byrne, D., Falkovich, G., and Shats, M. 2011. Upscale energy transfer in thick turbulent fluid layers. Nature Phys., 7(4), 321–324.CrossRefGoogle Scholar
Xu, H. T., Bourgoin, M., Ouellette, N. T., and Bodenschatz, E. 2006a. High order Lagrangian velocity statistics in turbulence. Phys. Rev. Lett., 96(2), 024503.CrossRefGoogle ScholarPubMed
Xu, H. T., Ouellette, N. T., and Bodenschatz, E. 2006b. Multifractal dimension of lagrangian turbulence. Phys. Rev. Lett., 96(11), 114503.CrossRefGoogle ScholarPubMed
Yaglom, A. M. 1957. Some classes of random fields in n-dimensional space, related to stationary random processes. Theor. Probab. Appl+, 2, 273–320.Google Scholar
Yaglom, A. M. 1966. The influence on the fluctuation in energy dissipation on the shape of turbulent characteristics in the inertial interval. Soviet Physics Dokladi, 2, 26–30.Google Scholar
Yeung, P. K. 2002. Lagrangian investigations of turbulence. Annu. Rev. Fluid Mech., 34(1), 115–142.CrossRefGoogle Scholar
Zhang, Q., Xu, C., Chen, Y. D., and Yu, Z. 2008. Multifractal detrended fluctuation analysis of streamflow series of the Yangtze River basin, China. Hydrol. Process., 22, 4997– 5003.CrossRefGoogle Scholar
Zhao, X., and He, G.-W. 2009. Space-time correlations of fluctuating velocities in turbulent shear flows. Phys. Rev. E, 79, 046316.CrossRefGoogle ScholarPubMed
Zhou, Q., and Xia, K.-Q. 2008. Comparative experimental study of local mixing of active and passive scalars in turbulent thermal convection. Phys. Rev. E, 77, 056312.CrossRefGoogle ScholarPubMed
Zhou, Q., and Xia, K.-Q. 2011. Disentangle plume-induced anisotropy in the velocity field in buoyancy-driven turbulence. J. Fluid Mech., 684, 192–203.CrossRefGoogle Scholar
Zhou, Q., Sun, C., and Xia, K.-Q. 2007. Morphological evolution of thermal plumes in turbulent Rayleigh-Bénard convection. Phys. Rev. Lett., 98, 074501.CrossRefGoogle ScholarPubMed
Zhou, Q., Xi, H. D., Zhou, S. Q., Sun, C., and Xia, K. Q. 2009. Oscillations of the largescale circulation in turbulent Rayleigh–Bénard convection: the sloshing mode and its relationship with the torsional mode. J. Fluid Mech., 630, 367–390.CrossRefGoogle Scholar
Zhou, Q., Li, C. M., Lu, Z. M., and Liu, Y. L. 2011. Experimental investigation of longitudinal space-time correlations of the velocity field in turbulent Rayleigh-Bénard convection. J. Fluid Mech., 683, 94–111.CrossRefGoogle Scholar
Zhou, S.-Q., and Xia, K.-Q. 2001. Scaling properties of the temperature field in convective turbulence. Phys. Rev. Lett., 87, 064501.CrossRefGoogle ScholarPubMed
Zhou, S.-Q., and Xia, K.-Q. 2002. Plume statistics in thermal turbulence: mixing of an active scalar. Phys. Rev. Lett., 89(18), 184502.CrossRefGoogle ScholarPubMed
Zolotarev, V. M. 1986. One-dimensional stable distributions. Vol. 65. American Mathematical Society.CrossRefGoogle Scholar
Zongo, S. B, and Schmitt, F. G. 2011. Scaling properties of pH fluctuations in coastal waters of the English Channel: pH as a turbulent active scalars. Nonlinear Proc. Geoph., 18, 829–839.CrossRefGoogle Scholar
Zongo, S. B., Schmitt, F. G., and Lefebvre, A. 2011. Observations biogéochimiques des eaux cˆotières à Boulogne-sur-mer à haute fréquence: les measures automatiques de la bouée MAREL,. 253–266.
Zybin, K. P., Sirota, V. A., Ilyin, A. S., and Gurevich, A. V. 2008. Lagrangian statistical theory of fully developed hydrodynamical turbulence. Phys. Rev. Lett., 100(17), 174504.CrossRefGoogle ScholarPubMed

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  • References
  • François G. Schmitt, Centre National de la Recherche Scientifique (CNRS), Paris, Yongxiang Huang
  • Book: Stochastic Analysis of Scaling Time Series
  • Online publication: 05 December 2015
  • Chapter DOI: https://doi.org/10.1017/CBO9781107705548.008
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  • References
  • François G. Schmitt, Centre National de la Recherche Scientifique (CNRS), Paris, Yongxiang Huang
  • Book: Stochastic Analysis of Scaling Time Series
  • Online publication: 05 December 2015
  • Chapter DOI: https://doi.org/10.1017/CBO9781107705548.008
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  • References
  • François G. Schmitt, Centre National de la Recherche Scientifique (CNRS), Paris, Yongxiang Huang
  • Book: Stochastic Analysis of Scaling Time Series
  • Online publication: 05 December 2015
  • Chapter DOI: https://doi.org/10.1017/CBO9781107705548.008
Available formats
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